As scandal captures much of Washington’s attention, the chairmen of the House and Senate Judiciary committees seem determined to move forward with immigration reform, despite the controversies that will inevitably demand much of their time.

For months, Democrats in the Senate have been pressing for quick action on what could be the body’s biggest legislative accomplishment this year. Even though Senate Judiciary Committee Chairman Patrick Leahy, D-Vt., has issued a statement saying he was “troubled” by news that the Justice Department had obtained phone records of Associated Press reporters, an aide to the committee said there are no plans to schedule a hearing on the issue that could disrupt the markup of the immigration bill, which is already underway.

The committee will begin its third day of markup Thursday, and intends to work through next week and possibly into the weekend to finish work before a recess at the end of the month.

But there could be resistance from Republicans, who are already mistrustful of the government’s willingness to enforce immigration laws. Senate “Gang of Eight” member Marco Rubio, R-Fla., said he was concerned because a “linchpin” of the reform bill is ensuring there is not another wave of illegal immigration, which depends on trust in the administration.

“We have already faced tremendous suspicion about the federal government’s ability or willingness to enforce the law,” Rubio said. “I think all these things we’ve been seeing in the press over the last few days, all they do is undermine confidence in the federal government even more, so I am concerned. Absolutely.”

Many Republicans who share that concern would have been a tough sell on immigration anyway, especially in the House, given that the Senate bill gives wide latitude to the Homeland Security Department on border control.

And if Republican leadership decides that focusing on a scandal-plagued administration is a better election strategy for 2014 than pursuing immigration reform and the potential demographic gains it could bring, they might win the messaging debate.

A Democratic aide argued that the scandals will allow members of Congress to assume a hyper-partisan stance on a multitude of issues (IRS, DOJ, and Benghazi), giving them room to act in a bipartisan manner when it comes to immigration. It’s a move perfected by Lindsey Graham, R-S.C., a member of the Gang of Eight, “to a T,” the aide said. Graham has hammered the administration over Benghazi, which has helped him stay in favor with conservative voters in his home state.

The House, meanwhile, has to prove it can do two things at once. Speaker John Boehner, R-Ohio, plans to abandon neither legislating nor investigating. “We have a twofold job here in the Congress,” he said.

On Thursday—one day after grilling Attorney General Eric Holder for hours—the members of the House Judiciary Subcommittee on Immigration and Border Security will hold hearings on two pieces of immigration legislation that deal with employment verification and agricultural workers. The committee will hold a hearing on the Senate immigration legislation next week, a committee aide said.